OpenMP* Threaded Functions and Problems

The following Intel® oneAPI Math Kernel Library function domains are threaded with the OpenMP* technology:

Direct sparse solver.
LAPACK.

For a list of threaded routines, see LAPACK Routines.
Level1 and Level2 BLAS.

For a list of threaded routines, see BLAS Level1 and Level2 Routines.
All Level 3 BLAS and all Sparse BLAS routines except Level 2 Sparse Triangular solvers.
All Vector Mathematics functions (except service functions).
FFT.

For a list of FFT transforms that can be threaded, see Threaded FFT Problems.

Product and Performance Information
Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex. Notice revision #20201201

Product and Performance Information

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.

Notice revision #20201201

LAPACK Routines

In this section, ? stands for a precision prefix of each flavor of the respective routine and may have the value of s, d, c, or z.

The following LAPACK routines are threaded with OpenMP*:

Linear equations, computational routines:
- Factorization: ?getrf, ?getrfnpi, ?gbtrf, ?potrf, ?pptrf, ?sytrf, ?hetrf, ?sptrf, ?hptrf
- Solving: ?dttrsb, ?gbtrs, ?gttrs, ?pptrs, ?pbtrs, ?pttrs, ?sytrs, ?sptrs, ?hptrs, ?tptrs, ?tbtrs
Orthogonal factorization, computational routines: ?geqrf, ?ormqr, ?unmqr, ?ormlq, ?unmlq, ?ormql, ?unmql, ?ormrq, ?unmrq
Singular Value Decomposition, computational routines: ?gebrd, ?bdsqr
Symmetric Eigenvalue Problems, computational routines: ?sytrd, ?hetrd, ?sptrd, ?hptrd, ?steqr, ?stedc.
Generalized Nonsymmetric Eigenvalue Problems, computational routines: chgeqz/zhgeqz.

A number of other LAPACK routines, which are based on threaded LAPACK or BLAS routines, make effective use of OpenMP* parallelism:
?gesv, ?posv, ?gels, ?gesvd, ?syev, ?heev, cgegs/zgegs, cgegv/zgegv, cgges/zgges, cggesx/zggesx, cggev/zggev, cggevx/zggevx, and so on.

Threaded BLAS Level1 and Level2 Routines

In the following list, ? stands for a precision prefix of each flavor of the respective routine and may have the value of s, d, c, or z.

The following routines are threaded with OpenMP*:

Level1 BLAS: ?axpy, ?copy, ?swap, ddot/sdot, cdotc, drot/srot
Level2 BLAS: ?gemv, ?trsv, ?trmv, dsyr/ssyr, dsyr2/ssyr2, dsymv/ssymv

Threaded FFT Problems

The following characteristics of a specific problem determine whether your FFT computation may be threaded with OpenMP*:

rank
domain
size/length
precision (single or double)
placement (in-place or out-of-place)
strides
number of transforms
layout (for example, interleaved or split layout of complex data)

Most FFT problems are threaded. In particular, computation of multiple transforms in one call (number of transforms > 1) is threaded. Details of which transforms are threaded follow.

One-dimensional (1D) transforms

1D transforms are threaded in many cases.

1D complex-to-complex (c2c) transforms of size N using interleaved complex data layout are threaded under the following conditions depending on the architecture:

Architecture	Conditions
Intel® 64	`N` is a power of 2, `log`₂(`N`) > 9, the transform is double-precision out-of-place, and input/output strides equal 1.
IA-32	`N` is a power of 2, `log`₂(`N`) > 13, and the transform is single-precision.
IA-32	`N` is a power of 2, `log`₂(`N`) > 14, and the transform is double-precision.
Any	`N` is composite, `log`₂(`N`) > 16, and input/output strides equal 1.

1D complex-to-complex transforms using split-complex layout are not threaded.

Multidimensional transforms

All multidimensional transforms on large-volume data are threaded.